Exchange

AtCoder

IDtenka1_2018_b

Time2000ms

Memory256MB

Difficulty—

In the beginning, Takahashi has $A$ cookies, and Aoki has $B$ cookies. They will perform the following operation alternately, starting from Takahashi: * If the number of cookies in his hand is odd, eat one of those cookies; if the number is even, do nothing. Then, give one-half of the cookies in his hand to the other person. Find the numbers of cookies Takahashi and Aoki respectively have after performing $K$ operations in total. ## Constraints * $1 \leq A,B \leq 10^9$ * $1 \leq K \leq 100$ * $A,B$ and $K$ are integers. ## Input Input is given from Standard Input in the following format: $A$ $B$ $K$ [samples]

Samples

Input #1

5 4 2

Output #1

5 3

The process will go as follows:

*   In the beginning, Takahashi and Aoki have $5$ and $4$ cookies, respectively.
*   Takahashi eats one cookie and gives two cookies to Aoki. They now have $2$ and $6$ cookies, respectively.
*   Aoki gives three cookies to Takahashi. They now have $5$ and $3$ cookies, respectively.

Input #2

3 3 3

Output #2

1 3

Input #3

314159265 358979323 84

Output #3

448759046 224379523

API Response (JSON)

{
  "problem": {
    "name": "Exchange",
    "description": {
      "content": "In the beginning, Takahashi has $A$ cookies, and Aoki has $B$ cookies. They will perform the following operation alternately, starting from Takahashi: *   If the number of cookies in his hand is odd,",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "tenka1_2018_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In the beginning, Takahashi has $A$ cookies, and Aoki has $B$ cookies. They will perform the following operation alternately, starting from Takahashi:\n\n*   If the number of cookies in his hand is odd,...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments